The tangent to the parabola y2=4x at the point where it intersects the circle x2+y2=5 in the first quadrant, passes through the point :
A
(−13,43)
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B
(−14,12)
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C
(34,74)
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D
(14,34)
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Solution
The correct option is C(34,74) y2=4x,x2+y2=5 The point of intersection of the two curves in the first quadrant is (1,2). Equation of tangent to the parabola y2=4x at (x1,y1)=(1,2) is yy1=4(x+x12) ⇒y=x+1 (34,74) passes through the line y=x+1